Practical Engineering Problems Research Articles

A Modified Sand Cat Swarm Optimization Algorithm Based on Multi-Strategy Fusion and Its Application in Engineering Problems

Addressing the issues of the sand cat swarm optimization algorithm (SCSO), such as its weak global search ability and tendency to fall into local optima, this paper proposes an improved strategy called the multi-strategy integrated sand cat swarm optimization algorithm (MSCSO). The MSCSO algorithm improves upon the SCSO in several ways. Firstly, it employs the good point set strategy instead of a random strategy for population initialization, effectively enhancing the uniformity and diversity of the population distribution. Secondly, a nonlinear adjustment strategy is introduced to dynamically adjust the search range of the sand cats during the exploration and exploitation phases, significantly increasing the likelihood of finding more high-quality solutions. Lastly, the algorithm integrates the early warning mechanism of the sparrow search algorithm, enabling the sand cats to escape from their original positions and rapidly move towards the optimal solution, thus avoiding local optima. Using 29 benchmark functions of 30, 50, and 100 dimensions from CEC 2017 as experimental subjects, this paper further evaluates the MSCSO algorithm through Wilcoxon rank-sum tests and Friedman’s test, verifying its global solid search ability and convergence performance. In practical engineering problems such as reducer and welded beam design, MSCSO also demonstrates superior performance compared to five other intelligent algorithms, showing a remarkable ability to approach the optimal solutions for these engineering problems.

A Modified Sand Cat Swarm Optimization Algorithm Based on Multi-Strategy Fusion and Its Application in Engineering Problems

Addressing the issues of the sand cat swarm optimization algorithm (SCSO), such as its weak global search ability and tendency to fall into local optima, this paper proposes an improved strategy called the multi-strategy integrated sand cat swarm optimization algorithm (MSCSO). The MSCSO algorithm improves upon the SCSO in several ways. Firstly, it employs the good point set strategy instead of a random strategy for population initialization, effectively enhancing the uniformity and diversity of the population distribution. Secondly, a nonlinear adjustment strategy is introduced to dynamically adjust the search range of the sand cats during the exploration and exploitation phases, significantly increasing the likelihood of finding more high-quality solutions. Lastly, the algorithm integrates the early warning mechanism of the sparrow search algorithm, enabling the sand cats to escape from their original positions and rapidly move towards the optimal solution, thus avoiding local optima. Using 29 benchmark functions of 30, 50, and 100 dimensions from CEC 2017 as experimental subjects, this paper further evaluates the MSCSO algorithm through Wilcoxon rank-sum tests and Friedman’s test, verifying its global solid search ability and convergence performance. In practical engineering problems such as reducer and welded beam design, MSCSO also demonstrates superior performance compared to five other intelligent algorithms, showing a remarkable ability to approach the optimal solutions for these engineering problems.

Flavoring search algorithm with applications to engineering optimization problems and robot path planning

In this paper, a human-based meta-heuristic algorithm, the Flavoring Search Algorithm, is proposed and mathematically modeled with the aim of providing an alternative optimization method for solving practical engineering problems. Flavoring Search Algorithm is inspired by the human behavior of flavoring in everyday life, including basic flavoring, formal flavoring, and auxiliary flavoring. By introducing a unique taste factor, it not only succeeded in making the Flavoring Search Algorithm corresponds to the real flavoring process but also balanced the exploration and exploitation of the algorithm. With the help of the taste factors, Flavoring Search Algorithm performs basic flavoring (initial flavoring and random flavoring) in the exploration phase and formal flavoring and auxiliary flavoring in the exploitation phase. In addition, theoretical analysis and experiments have led to the conclusion that the taste factor can be used as an effective and practical new threshold conversion mechanism for meta-heuristic algorithms. This study also establishes a Markov model to rigorously analyze the Flavoring Search Algorithm as a globally convergent algorithm from a mathematical point of view. Through experimental and analytical comparisons with other excellent optimizers on 30 test functions, as well as on 3 real-world engineering design problems and 1 path planning problem. The results show that the Flavoring Search Algorithm generally outperforms the tested competitors in solving benchmark functions and engineering problems, validating the utility of the proposed optimizer in solving challenging real-world problems.

Multi‐strategy Grey Wolf Optimizer for Engineering Problems and Sewage Treatment Prediction

Grey wolf optimizer (GWO) is a highly valued heuristic algorithm in many fields. However, for some complex problems, especially high‐dimensional and multimodal problems, the basic algorithm has limited computational power and cannot get a satisfactory answer. In order to find a better solution, an improved algorithm based on GWO is proposed herein. Gaussian barebone, random selection and chaotic game mechanisms are introduced into the GWO algorithm to enhance the global search ability. The GWO enhanced by three mechanisms is called CBRGWO. To verify the performance of CBRGWO, using IEEE CEC 2017 as a test function, CBRGWO is compared to five GWO variants, five basic algorithms, six advanced algorithms, and four champion algorithms. CBRGWO is evaluated using the Friedman test and Wilcoxon signed‐rank test. Then, the stability of CBRGWO is analyzed. To verify that CBRGWO is still effective in practical application, CBRGWO is applied to five engineering problems and a water quality prediction problem. The experimental findings indicate that CBRGWO maintains excellent optimization ability in practical engineering problems.

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

The main objective of this paper is to reduce the dimensionality of unknown coefficient vectors of finite-element (FE) solutions in two-grid (CN) FE (TGCNFE) format for the nonlinear unsaturated soil water flow problem by using a proper orthogonal decomposition (POD) and to design a new reduced-dimension iteration TGCNFE (RDITGCNFE). For this objective, a new time semi-discrete CN (TSDCN) scheme for the nonlinear unsaturated soil water flow problem is first designed and the existence, stability, and error estimates of TSDCN solutions are demonstrated. Subsequently, a new TGCNFE format for the nonlinear unsaturated soil water flow problem is designed and the existence, unconditional stability, and error estimates of TGCNFE solutions are demonstrated. Next, a new RDITGCNFE format with the same FE basis functions as the TGCNFE format is built by the POD method and the existence, unconditional stability, and error estimates of RDITGCNFE solutions are discussed. Ultimately, the rightness of theory results and the superiority of the RDITGCNFE format are verified by two sets of numerical tests. It is worth noting that the RDITGCNFE format differs completely from all previous reduced-dimension methods, including the authors’ previous works. Therefore, the study of this paper can not only provide a new theoretical method for the dimensionality reduction of numerical models for nonlinear problems but also provide an algorithm implementation technology for the numerical simulation of practical engineering problems.

An Improved Boundary Element Method for Predicting Half-Space Scattered Noise Combined with Permeable Boundaries

The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.

On the elastic–plastic behaviors of centrifugal steam compressor impeller under cyclic thermomechanical loading

AbstractIn this paper, the cyclic elastic–plastic behaviors of the centrifugal steam compressor impeller (CSCI) structure under practical operating conditions are discussed employing the linear matching method (LMM). The three‐stage strategy of the LMM is employed to determine the shakedown and ratchet boundaries by conducting a series of iterative direct steady cyclic analysis, and based on this, the load regions corresponding to different types of damage behavior that may occur during the operation are identified. Computational results reveal slight contraction in the structural response diagram when considering actual material constitutive relationships, compared to ideal elastic–plastic models. Meanwhile, by integrating the unified ratchet and fatigue program with fatigue experimental data, a series of constant low‐cycle fatigue life curves has been presented for different service conditions. Furthermore, a comparison with detailed step‐by‐step inelastic analyses confirms the applicability and great efficiency of the LMM in practical engineering problems.

Selection of Mathematical Optimization Methods for Solving Engineering Practice Problems

Selection of Mathematical Optimization Methods for Solving Engineering Practice Problems

Novel study on active reliable PID controller design based on probability density evolution method and interval-oriented sequential optimization strategy

Vibration active control is a significant problem in practical engineering, but the influence of hybrid uncertainties in practical engineering cannot be ignored. For the uncertainties with adequate data, probability theory can be used while for the uncertainties with insufficient data, probability theory is limited and interval quantification can be used. Taking the widely used proportional-integral-differential (PID) control as an example, a novel study on controller design based on probability density evolution method and interval-oriented sequential optimization strategy considering interval and random uncertainties is proposed. Firstly, under a certain sample point of interval uncertainties, probability density evolution equation is utilized to calculate the probability density function of uncertain response considering only random uncertainties. In this way the probabilistic reliability corresponding to the sample point can be obtained. Then the hybrid reliability is defined as the average probability within the interval uncertainty and the adaptive dichotomy method is utilized to choose proper sample points of interval uncertainties, in which the reliability curve and the interval uncertainty axis is regarded as the judgement of convergence. Next the hybrid reliability is introduced to the optimization as a constraint and the PID gains reliable design optimization is established to balance the energy-consuming and safety. Finally, the sequential optimization strategy is adopted to improve the efficiency of optimization. In every iteration step of the optimization, the constraint of deterministic optimal design is adjusted according to the static reliability at the moment before the passage or reaching the maximum value. Three numerical examples are presented to demonstrate the accuracy and practicability of the proposed framework.

Numerical method for the form finding and force analysis of non-prestressed cable-membrane structures with mechanism displacement

The non-prestressed cable-membrane structures exhibit significant nonlinear characteristics such as mechanism displacement and large deformation under external loads. Analyzing such structural behaviors using traditional finite element analysis methods is challenging due to the singularity of the stiffness matrix and the non-convergence of the iterations. In this study, a numerical method based on the vector form intrinsic finite element (VFIFE) method for form finding and force analysis of non-prestressed cable-membrane structures with mechanism displacement is introduced. First, the basic principle and calculation process for analyzing the deformation and internal force of cable-membrane structures are introduced. Second, the applicability of the present method is demonstrated by four numerical examples, including static analysis of the double parabolic inflated membrane and the hemispherical inflated cable-membrane, mechanism motion simulation of the cloth, and large deformation calculation for the flexible curtain. Finally, a spatial non-prestressed cable-membrane model experiment is performed. The effectiveness of VFIFE method is further validated by comparing the measured displacement and internal force to the numerical results. It is shown that the numerical method proposed in this study can effectively simulate the morphological evolution and internal force distribution for the flexible cable-membrane structures with large mechanism displacement, providing a reference for analyzing such practical engineering problems involving strongly nonlinear characteristics.

Improved Driving Training-Based Optimization Algorithm Using Levy Flight and Crowding Distance Techniques

This study presents an improved version of the Driving Training-Based Optimization (DTBO) algorithm, the Improved Driving Training-Based Optimization (IDTBO). The work addresses fundamental issues in selecting drivers and learners for the conventional DTBO, which substantially impact the algorithm's accuracy and convergence speed. Two significant improvements are proposed: including the crowding distance technique for more diverse driver and learner selection and incorporating the Levy Flight distribution for better exploration and local optima avoidance. The IDTBO's performance is evaluated using twelve benchmark functions, including unimodal and high-dimensional multimodal optimization functions. The results indicate that IDTBO performs exceptionally well, with more extraordinary exploitation ability on unimodal functions and consistent achievement of the global optima. The proposed IDTBO demonstrated exceptional exploration capabilities on high-dimensional multimodal functions and performed competitively with other algorithms in the literature. From six functions, the IDTBO obtained zero optimal values. Again, the rate of convergence analysis demonstrates that IDTBO finds optimal solutions in fewer iterations, demonstrating its capacity to balance exploration and exploitation. To assess the strength of the IDTBO in solving real-world problems, the improved DTBO is further tested on two practical benchmark engineering problems. The IDTBO again produced a competitive performance against other algorithms in the literature. The study shows that IDTBO is a valuable metaheuristic algorithm that can tackle various real-world optimization problems.

Characteristics of Pre-peak Mechanical Damage and Energy Evolution of Typical Hard-rock in Diversion Tunnel under Cyclic Loading-Unloading

An in-depth understanding of the pre-peak mechanical damage and energy-evolution characteristics of typical hard-rock in a diversion tunnel under cyclic load is of great significance to promote the safe and efficient construction of the diversion tunnel and the stability of surrounding rock. To study the pre-peak mechanical characteristics and the competition mechanism between energy storage and energy dissipation of typical hard-rock in a diversion tunnel under cyclic loading-unloading, combined with the internal drilling and blasting excavation of the actual engineering rock mass and the external vehicle cyclic load environment of the diversion tunnel, the cyclic loadingunloading tests of typical granite and tuff in diversion tunnel were carried out. Based on the analysis principle of mechanics and energy, the strain variables, modulus variables, energy variables and damage variables of granite and tuff under cyclic loading-unloading test were defined. The cyclic mechanical properties and energyevolution characteristics of granite and tuff under pre-peak load were analyzed. The competition mechanism between pre-peak energy storage and pre-peak energy dissipation of granite and tuff and the evolution law of strain damage variable and energy damage variable were revealed. The selection principle of rock sample size and the limitation of the test scheme were further discussed. The study of the damage evolution of rocks close to failure (pre-peak stage) under cyclic load is helpful to better understand the damage and failure mechanism of rocks in practical engineering problems. Keywords: Diversion tunnel, Cyclic loading-unloading, Granite/Tuff, Blasting cyclic load, Energy evolution.

A hybrid particle swarm optimization algorithm for solving engineering problem

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function (f1-f13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{1}-{f}_{13}$$\\end{document}) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

Networked Evolutionary Game-Based Demand Response via Feedback Controls

In this paper, the demand response considering interactive decision making between residential users and utility companies is modelled and controlled using networked evolutionary game (NEG) theory. The NEG is achieved via a widely used mathematical tool, namely the semi-tensor product (STP) of matrices, through which, feedback controls can be implemented to dynamically regulate the game-based networks. Firstly, the dynamic interactions between utility companies who provide various energy consumption packs and residential users who can intelligently choose preferable packs are modelled in the state-space form, in which both sides are consistently pursuing their maximum payoffs. Then, a quantitive analysis of such system’s equilibria is conducted using rigorous mathematical derivations, followed by the design of a profile feedback controller when the existing equilibria are not satisfactory towards the required energy consumption. Finally, an illustrative example is demonstrated, where the dynamic gaming between utility companies and users is illustrated and the effectiveness of the proposed feedback control is validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper addresses a very practical engineering problem, which is the demand response in the modern smart grid. Different from general optimization approaches in the existing works, the method proposed by this paper improves the demand response via feedback control of networked systems, which is based on the rigorous matrix approaches via state space equations. In addition, the work in this paper considers very practical factors in actual engineering (i.e., users with different action choices and decision logics being all together), which also provides much value to practitioners than the relevant works with similar theoretical approaches. The method proposed in this paper provides an effective regulation of the demand response in practice and can be flexibly adjusted according to actual situations.

A novel linear regression density peak clustering‐based transmission line protection for line‐commuted converter‐voltage source converter hybrid high voltage direct current system

AbstractLine‐commuted converter (LCC)–voltage source converter (VSC) hybrid high voltage direct current (HVDC) transmission system is an innovative technology, the existing LCC and VSC protection require setting, and it is difficult to be directly applied in the LCC–VSC hybrid HVDC, which is a serious problem in practical engineering. A novel linear regression density peak clustering (LRDPC) approach is introduced for transmission line protection. LRDPC employs Least Squares linear regression to compute the fault current slope, followed by density peak clustering for fault type identification. The proposed protection structure is straightforward and setting‐less, eliminating the need for fault pole selection elements and classification thresholds. Validation on the Kun‐Liu‐Long LCC–VSC HVDC RTDS system demonstrates the method's effectiveness in identifying diverse faults under varying conditions, including fault types, locations, resistances, and signal‐to‐noise ratios. Notably, it remains robust against fault impedance (600 Ω) and noise interference (20 dB).

Estimating the optimal duration of random loading as part of machine part durability research

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

Modified Structure of Deep Neural Network for Training Multi-Fidelity Data With Non-Common Input Variables

Abstract Multi-fidelity surrogate (MFS) modeling technology, which efficiently constructs surrogate models using low-fidelity (LF) and high-fidelity (HF) data, has been studied to enhance the predictive capability of engineering performances. In addition, several neural network (NN) structures for MFS modeling have been introduced, benefiting from recent developments in deep learning research. However, existing multi-fidelity (MF) NNs have been developed assuming identical sets of input variables for LF and HF data, a condition that is often not met in practical engineering systems. Therefore, this study proposes a new structure of composite NN designed for MF data with different input variables. The proposed network structure includes an input mapping network that connects the LF and HF data's input variables. Even when the physical relationship between these variables is unknown, the input mapping network can be concurrently trained during the process of training the whole network model. Customized loss functions and activation variables are suggested in this study to facilitate forward and backward propagation for the proposed NN structures when training MF data with different inputs. The effectiveness of the proposed method, in terms of prediction accuracy, is demonstrated through mathematical examples and practical engineering problems related to tire performances. The results confirm that the proposed method offers better accuracy than existing surrogate models in most problems. Moreover, the proposed method proves advantageous for surrogate modeling of nonlinear or discrete functions, a characteristic feature of NN-based methods.

Arching development above active trapdoor: insight from multi-scale analysis using FEM–SPH

AbstractUnderground excavation is usually accompanied by complex soil-structure interaction problems in practical engineering. This paper develops a novel multi-scale approach for investigating the soil arching effect through trapdoor tests. This approach adopts the finite element method (FEM) and smoothed particle hydrodynamics (SPH) method to handle the particle-rigid body interaction in the trapdoor tests, incorporating a micromechanical 3D-H model to derive the nonlinear material response required by the SPH method. The variation of the earth pressure on the trapdoor in simulations exhibits good agreement with those of the experiments. Extensive parametric analyzes are performed to assess the effects of soil height and inter-particle friction angle on the evolution of load transfer and soil deformation. Three deformation patterns are observed under different buried conditions, including the trapezoid, the triangle, and the equal settlement pattern. Results indicate that the planes of equal settlement develop progressively with the trapdoor movement and then enter the range of experimentally observed values. Additionally, three failure mechanisms are identified that correspond to the three deformation patterns. Due to the advantages of the micromechanical model, mesoscale behavior is captured. The anisotropy of stress distribution in the plastic region is found during the arching process.

A closed-form expression of a ductile Fracture Limit Surface (FLS) for general plane stress deformation paths

Ductile fracture in metals is a complex phenomenon caused by the nucleation, growth, and aggregation of micron-sized voids. Existing theoretical models for fracture use experimentally determined Fracture Limit Curves (FLCs) in two-dimensional strain space, which require multiple curves to account for anisotropic effects. This paper proposes a practical closed-form analytical function for a Fracture Limit Surface (FLS) which has a conical shape in the Elastic Distortional Deformation Space (EDDS). The EDDS is a space generated by the components of the elastic distortional metric of the microstructural vectors that characterize elastic distortional deformations and the orientations of anisotropy. The FLS is determined by simulating only four experimental FLCs using a large deformation Eulerian formulation of the microstructural vectors and it depends only on the current state of elastic distortional deformation. It is shown that the failure limit points predicted by the FLS agreed very well with those predicted using a popular evolution equation for damage-based ductile fracture. Path-independence of the FLS is also examined using experimental data. In addition, the example of a B-pillar forming process is presented to show that the FLS can be applied to practical engineering problems with material points that experience general loading paths.

APSO-SL: An Adaptive Particle Swarm Optimization with State-Based Learning Strategy

Particle swarm optimization (PSO) has been extensively used to solve practical engineering problems, due to its efficient performance. Although PSO is simple and efficient, it still has the problem of premature convergence. In order to address this shortcoming, an adaptive particle swarm optimization with state-based learning strategy (APSO-SL) is put forward. In APSO-SL, the population distribution evaluation mechanism (PDEM) is used to evaluate the state of the whole population. In contrast to using iterations to just the population state, using the population spatial distribution is more intuitive and accurate. In PDEM, the population center position and best position for calculation are used for calculation, greatly reducing the algorithm’s computational complexity. In addition, an adaptive learning strategy (ALS) has been proposed to avoid the whole population’s premature convergence. In ALS, different learning strategies are adopted according to the population state to ensure the population diversity. The performance of APSO-SL is evaluated on the CEC2013 and CEC2017 test suites, and one engineering problem. Experimental results show that APSO-SL has the best performance compared with other competitive PSO variants.